Solve for $x$ and $y$ using elimination. ${3x-2y = -3}$ ${-5x+2y = -3}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {3x-2y = -3}\thinspace$ to find $y$ ${3}{(3)}{ - 2y = -3}$ $9-2y = -3$ $9{-9} - 2y = -3{-9}$ $-2y = -12$ $\dfrac{-2y}{{-2}} = \dfrac{-12}{{-2}}$ ${y = 6}$ You can also plug ${x = 3}$ into $\thinspace {-5x+2y = -3}\thinspace$ and get the same answer for $y$ : ${-5}{(3)}{ + 2y = -3}$ ${y = 6}$